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A202372 Number of (n+2)X4 binary arrays avoiding patterns 001 and 111 in rows and columns.

%I A202372 #7 Jul 22 2025 16:33:09
%S A202372 257,824,2293,5677,13751,31240,68965,148281,310793,640839,1299608,
%T A202372 2601118,5148674,10088995,19604270,37808312,72431966,137955751,
%U A202372 261370700,492867363,925469673,1731093570,3226750237,5995509954,11107634611
%N A202372 Number of (n+2)X4 binary arrays avoiding patterns 001 and 111 in rows and columns.
%C A202372 Column 2 of A202378
%H A202372 R. H. Hardin, <a href="/A202372/b202372.txt">Table of n, a(n) for n = 1..210</a>
%F A202372 Empirical: a(n) = 3*a(n-1) +5*a(n-2) -12*a(n-3) -34*a(n-4) +30*a(n-5) +110*a(n-6) +16*a(n-7) -230*a(n-8) -171*a(n-9) +177*a(n-10) +360*a(n-11) +66*a(n-12) -172*a(n-13) -248*a(n-14) -135*a(n-15) -72*a(n-16) +182*a(n-17) +196*a(n-18) +148*a(n-19) -68*a(n-20) -39*a(n-21) -106*a(n-22) -13*a(n-23) -46*a(n-24) +29*a(n-25) -34*a(n-26) +16*a(n-27) -5*a(n-28) +42*a(n-29) +13*a(n-30) +22*a(n-31) -8*a(n-32) -6*a(n-33) -14*a(n-34) -3*a(n-35) -2*a(n-36) +2*a(n-37) +a(n-38) +a(n-39)
%e A202372 Some solutions for n=7
%e A202372 ..1..1..0..1....1..1..0..1....1..0..1..1....1..1..0..1....1..1..0..0
%e A202372 ..1..0..1..1....0..0..0..0....0..1..1..0....1..0..1..0....0..1..1..0
%e A202372 ..0..1..0..0....1..1..0..1....1..0..0..0....0..1..1..0....1..0..0..0
%e A202372 ..1..0..1..0....0..1..0..1....0..1..0..0....1..0..0..0....1..1..0..0
%e A202372 ..0..1..0..0....1..0..0..0....0..0..0..0....1..0..0..0....0..1..0..0
%e A202372 ..1..0..0..0....1..1..0..0....0..0..0..0....0..0..0..0....1..0..0..0
%e A202372 ..1..1..0..0....0..1..0..0....0..0..0..0....1..0..0..0....0..1..0..0
%e A202372 ..0..1..0..0....1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A202372 ..0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%K A202372 nonn
%O A202372 1,1
%A A202372 _R. H. Hardin_ Dec 18 2011